Solved 2024 Specimen Paper ICSE Class 10 Mathematics — Question 2

Given, equation : x² - 4x - 2 = 0.

By formula,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values we get :

$\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1\times -2}}{2 \times 1} \\[1em] = \dfrac{4 \pm \sqrt{16 + 8}}{2} \\[1em] = \dfrac{4 \pm \sqrt{24}}{2} \\[1em] = \dfrac{4 \pm 2\sqrt{6}}{2} \\[1em] = 2 \pm \sqrt{6} \\[1em] = 2 + \sqrt{6}, 2 - \sqrt{6} \\[1em] = 2 + 2.449, 2 - 2.449 \\[1em] = 4.449, -0.449$

Hence, x = 4.449 or -0.449